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Two Factor Additive Conjoint Measurement with One Solvable Component.

Gonzales1

  • 1LIP6, Université Paris 6, Paris, France

Journal of Mathematical Psychology
|June 1, 2000
PubMed
Summary
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This study explores additive separable utilities, finding that higher-order cancellation axioms are generally necessary for additive representability. A special case shows independence axioms suffice, with unique representations following Fishburn

Area of Science:

  • Decision Theory
  • Utility Theory
  • Mathematical Economics

Background:

  • Additive separable utilities are fundamental in economic modeling.
  • Existing representation theorems often rely on strong independence axioms.
  • The necessity of higher-order cancellation axioms for additive representability is explored.

Purpose of the Study:

  • To investigate the conditions required for the existence of additive separable utilities.
  • To determine the role of cancellation axioms in ensuring additive representability.
  • To extend findings from two-dimensional spaces to n-dimensional spaces.

Main Methods:

  • Analysis of restricted solvability in Cartesian products.
  • Development of a generic family of counterexamples.

Related Experiment Videos

  • Examination of the relationship between mth and (m+1)st order cancellation axioms.

    • Main Results:

    • Additive representability generally requires cancellation axioms of any order.
    • The (m+1)st order cancellation axiom is not derivable from the mth order axiom when m is even.
    • In a special case, additive representations are derivable from the independence axiom alone.

    Conclusions:

    • Higher-order cancellation axioms are crucial for additive separable utility representation.
    • The findings refine understanding of utility representation theorems.
    • Representations exhibit Fishburn's (1981) uniqueness property, differing from classical theorems.